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arXiv · 2609.01010

Sum-of-Squares Certificates for Copositive Matrices via Recursive Identities: The de Klerk-Pasechnik Conjecture and Hoffman--Pereira Matrices

Jineon Baek·Luis Felipe Vargas
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Abstract

We establish the conjecture by de Klerk and Pasechnik (2002), claiming that the semidefinite bounds $\vartheta^{(r)}(G)(r\geq 0)$ for the stability number $\alpha(G)$ are exact at $r=\alpha(G)-1$, by exhibiting an explicit sum-of-squares certificate. This certificate allows us to recover a known characterization of the minimizers of the Motzkin-Straus formulation for $1/\alpha(G)$. Additionally, we give sum-of-squares copositivity certificates for the matrices satisfying the Hoffman--Pereira sign condition, a crucial condition for characterizing copositive matrices with $\{-1,0,1\}$ entries.

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Jineon Baek, Luis Felipe Vargas. 2026-09-01. Sum-of-Squares Certificates for Copositive Matrices via Recursive Identities: The de Klerk-Pasechnik Conjecture and Hoffman--Pereira Matrices. https://arxiv.org/abs/2609.01010

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